Ketosis alone, probably not. If you think of ketosis as a biomarker for glycogen depletion and very low insulin, it's a good indication that you have prime conditions for lipolysis (but not essential for it). As Darryl notes, that doesn't mean much for fat oxidation if you aren't taking in fewer calories than your body needs (but most people on Atkins do so spontaneously, at least at the beginning).

Note on terms: To lose fat you need to mobilize it (lipolysis) and burn it (oxidation).